Multiple positive solutions for nonlinear dynamical systems on a measure chain

摘要

In this paper, we consider the following dynamical system on a measure chain: u1ΔΔ(t)+f1(t,u1(σ(t)),u2(σ(t)))=0,t∈[a,b],u2ΔΔ(t)+f2(t,u1(σ(t)),u2(σ(t)))=0,t∈[a,b],with the Sturm–Liouville boundary value conditionsαui(a)−βuiΔ(a)=0,γui(σ(b))+δuiΔ(σ(b))=0fori=1,2.Some results are obtained for the existence of three positive solutions of the above problem by using Leggett–Williams fixed point theorem.